If a customer suggests an improvement, who owns the invention?

Ownership follows inventorship, and inventorship follows conception, not payment or suggestion. If a customer says it would be great if the product could also do X and your engineers work out how, your engineers are the inventors and, under their assignment agreements, your company owns it. If the customer's engineer works out how, describing the specific technical means that end up in a claim, that engineer is an inventor, or a joint inventor alongside yours, and their employer will usually own their share under the customer's own employment agreements. Naming only your own staff on the application when a customer's engineer contributed to a claim is an inventorship error that can put the patent's validity at risk (see MPEP 2109), so the question has to be answered honestly at filing.

The way to keep ownership clear is contractual and evidential. A feedback clause in the customer agreement grants you a perpetual, royalty-free, irrevocable licence to use any suggestions, ideas or feedback and, better still, an assignment of any IP in them; most customers accept this because they want the improvement built. An invention record kept as the work happens, showing who proposed the problem and who worked out the solution, settles inventorship questions that would otherwise depend on memory two years later. Where a customer's engineer did genuinely co-invent, the options are an assignment from the customer, a cross-licence, or a joint ownership agreement that fixes who may license and enforce. What not to do is leave it undocumented: a joint inventor discovered in due diligence, whose employer has never assigned their interest, is exactly the kind of chain-of-title gap that stalls a financing. See also Who owns IP created in a pilot or joint development project?